Problem: This is the easy version of the problem. The difference between the versions is that in the easy version all prices a_i are different. You can make hacks if and only if you solved both versions of the problem.

Today is Sage's birthday, and she will go shopping to buy ice spheres. All n ice spheres are placed in a row and they are numbered from 1 to n from left to right. Each ice sphere has a positive integer price. In this version all prices are different.

An ice sphere is cheap if it costs strictly less than two neighboring ice spheres: the nearest to the left and the nearest to the right. The leftmost and the rightmost ice spheres are not cheap. Sage will choose all cheap ice spheres and then buy only them.

You can visit the shop before Sage and reorder the ice spheres as you wish. Find out the maximum number of ice spheres that Sage can buy, and show how the ice spheres should be reordered.

Input

The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of ice spheres in the shop.

The second line contains n different integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the prices of ice spheres.

Output

In the first line print the maximum number of ice spheres that Sage can buy.

In the second line print the prices of ice spheres in the optimal order. If there are several correct answers, you can print any of them.

Example

Input


5
1 2 3 4 5


Output


2
3 1 4 2 5 

Note

In the example it's not possible to place ice spheres in any order so that Sage would buy 3 of them. If the ice spheres are placed like this (3, 1, 4, 2, 5), then Sage will buy two spheres: one for 1 and one for 2, because they are cheap.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
//import java.lang.*;

public class ranjan{

    public static Read cin;
    //public static InputReader cin;
    public static PrintWriter cout;
    public static boolean[] safe;
    public static final long bil = (long)1e9+7;
    public static int fileread = 0; 
    
    public static void main(String ...arg) throws IOException
    {
        /*console writer*/
        cout = new PrintWriter(new BufferedOutputStream(System.out));
        /*Debug Reader*/
        //Scan cin =new Scan();
        if(fileread == 1)
        {
            try
            {
            cin = new Read(new FileInputStream(new File("in1.txt")));
            //cin = new InputReader(new FileInputStream(new File("in1.txt")));
            }
            catch (IOException error){}
        }
        else{
            cin = new Read(System.in);
            //cin = new InputReader(System.in);
        }

        int n = cin.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<n;i++) arr[i] = cin.nextInt();
		Arrays.sort(arr);
		int i=0,j=n-1;
		cout.print((n%2==0?n/2-1:n/2) + "\n");
		while(i<j)
			cout.print(arr[j--] + " " + arr[i++] + " ");
		if((n&1) == 1)
				cout.print(arr[n/2]);
		cout.close();
    }

	private static class Pair{
		public int a,b;
		public Pair(int a,int b)
		{
			this.a = a;
			this.b = b;
		}	
	}


    /*public static void seive(int size)
    {
        prime[0] = prime[1] = false;
        int p = 2;
        while(p*p<= size)
        {
            if(prime[p])
            {
                for(int i=p*p;i<size;i += p)
                    prime[i] = false;
            }
            p++;
        }
    }*/


    public static <K, V> V getOrDefault(HashMap<K,V> map, K key, V defaultValue) {
        return map.containsKey(key) ? map.get(key) : defaultValue;
    }
    
    static void reverseArray(int intArray[], int size) 
    { 
        int i, temp; 
        for (i = 0; i < size / 2; i++) { 
            temp = intArray[i]; 
            intArray[i] = intArray[size - i - 1]; 
            intArray[size - i - 1] = temp; 
        }  
    } 

    public static long mod_pow(long x,long n,long mod) {
        long res=1;
        while(n>0) {
            if((n&1)==1)res=res*x%mod;
            x=x*x%mod;
            n>>=1;
        }
        return res;
    }
    public static int gcd(int n1, int n2) 
    {
        int r;
        while (n2 != 0) 
        {
            r = n1 % n2;
            n1 = n2;
            n2 = r;
        }
        return n1;
    }
 
    /*public static int lcm(int n1, int n2) 
    {
        int answer = (n1 * n2) / (gcd(n1, n2));
        return answer;
    }*/


    static class InputReader {
        final InputStream is;
        final byte[] buf = new byte[1024];
        int pos;
        int size;
 
        public InputReader(InputStream is) {
            this.is = is;
        }
 
        public int nextInt() {
            int c = read();
            while (isWhitespace(c))
                c = read();
            int sign = 1;
            if (c == '-') {
                sign = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                c = read();
            } while (!isWhitespace(c));
            return res * sign;
        }
 
        int read() {
            if (size == -1)
                throw new InputMismatchException();
            if (pos >= size) {
                pos = 0;
                try {
                    size = is.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (size <= 0)
                    return -1;
            }
            return buf[pos++] & 255;
        }
 
        static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
    }

static class RecursionLimiter {
    public static long maxLevel = 100000L;

    public static void emerge() {
        if (maxLevel == 0)
            return;
        try {
            throw new IllegalStateException("Too deep, emerging");
        } catch (IllegalStateException e) {
            if (e.getStackTrace().length > maxLevel + 1)
                throw e;
        }
    }
}


static class Scan {
        private byte[] buf=new byte[1024];
        private int index;
        private InputStream in;
        private int total;
        public Scan()
        {
            in=System.in;
        }
        public int scan()throws IOException
        {
            if(total<0)
            throw new InputMismatchException();
            if(index>=total)
            {
                index=0;
                total=in.read(buf);
                if(total<=0)
                return -1;
            }
            return buf[index++];
        }
        public int scanInt()throws IOException
        {
            int integer=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n))
            {
                if(n>='0'&&n<='9')
                {
                    integer*=10;
                    integer+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            return neg*integer;
        }
        public double scanDouble()throws IOException
        {
            double doub=0;
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            int neg=1;
            if(n=='-')
            {
                neg=-1;
                n=scan();
            }
            while(!isWhiteSpace(n)&&n!='.')
            {
                if(n>='0'&&n<='9')
                {
                    doub*=10;
                    doub+=n-'0';
                    n=scan();
                }
                else throw new InputMismatchException();
            }
            if(n=='.')
            {
                n=scan();
                double temp=1;
                while(!isWhiteSpace(n))
                {
                    if(n>='0'&&n<='9')
                    {
                        temp/=10;
                        doub+=(n-'0')*temp;
                        n=scan();
                    }
                    else throw new InputMismatchException();
                }
            }
            return doub*neg;
        }
        public String scanString()throws IOException
        {
            StringBuilder sb=new StringBuilder();
            int n=scan();
            while(isWhiteSpace(n))
            n=scan();
            while(!isWhiteSpace(n))
            {
                sb.append((char)n);
                n=scan();
            }
            return sb.toString();
        }
        private boolean isWhiteSpace(int n)
        {
            if(n==' '||n=='\n'||n=='\r'||n=='\t'||n==-1)
            return true;
            return false;
        }
    }

}

class Read
{
    private BufferedReader br;
    private StringTokenizer st;

    public Read(InputStream is)
    { br = new BufferedReader(new InputStreamReader(is)); }

    String next()
    {
        while (st == null || !st.hasMoreElements())
        {
            try {st = new StringTokenizer(br.readLine());}
            catch(IOException e)
                {e.printStackTrace();}
        }
        return st.nextToken();
    }

    int nextInt()
    { return Integer.parseInt(next()); }

    long nextLong()
    { return Long.parseLong(next()); }

    double nextDouble()
    { return Double.parseDouble(next()); }

    String nextLine()
    {
        String str = "";
        try {str = br.readLine();}
        catch(IOException e)
            {e.printStackTrace();}
        return str;
    }
}